Chapter 7: Q14. (page 460)

Simplify each expression.
${(6 x^{3} y^{2})}^{2}$

Short Answer

Expert verified

The expression ${(6 x^{3} y^{2})}^{2}$ can be simplified as width="53">36x6y4.

Step by step solution

Step 1. Write property of power of a product.

For any real number x, y and any integer n, ${(x y)}^{n} = x^{n} y^{n}$ .

Step 2. Apply the property of power of a product.

Apply the property of power of a product to the given expression.

$6^{2} {(x^{3})}^{2} {(y^{2})}^{2}$

Step 3. Write the property of power of a power.

For any real number a and any integers m and n, ${(a^{m})}^{n} = a^{m \cdot n}$

Step 4. Apply the property of power of a power.

Apply the property of power of a power to the expression in step 2.

$6^{2 \cdot 1} x^{3 \cdot 2} y^{2 \cdot 2}$

Step 5. Simplify the obtained expression.

Simplify the expression in step.

$36 x^{6} y^{4}$

Therefore, ${(6 x^{3} y^{2})}^{2}$ can be simplified to $36 x^{6} y^{4}$ .

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Simplify each expression.
${(6 x^{3} y^{2})}^{2}$

Short Answer

Step by step solution

Step 1. Write property of power of a product.

Step 2. Apply the property of power of a product.

Step 3. Write the property of power of a power.

Step 4. Apply the property of power of a power.

Step 5. Simplify the obtained expression.

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Simplify each expression.6x3y22

Short Answer

Step by step solution

Step 1. Write property of power of a product.

Step 2. Apply the property of power of a product.

Step 3. Write the property of power of a power.

Step 4. Apply the property of power of a power.

Step 5. Simplify the obtained expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression.
${(6 x^{3} y^{2})}^{2}$